{
 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "# BDM1-P0 Element for Poisson Equation in 2D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example is to show the rate of convergence of the BDM1-P0 mixed finite element approximation of the Poisson equation on the unit square:\n",
    "\n",
    "$$- \\nabla (d \\nabla) u = f \\; \\hbox{in } (0,1)^2$$\n",
    "\n",
    "for the following boundary conditions\n",
    "- pure Dirichlet boundary condition: $u = g_D \\text{ on } \\partial \\Omega$.\n",
    "- Pure Neumann boundary condition: $d\\nabla u\\cdot n=g_N \\text{ on } \\partial \\Omega$.\n",
    "- mixed boundary condition: $u=g_D \\text{ on }\\Gamma_D, \\nabla u\\cdot n=g_N \\text{ on }\\Gamma_N.$\n",
    "\n",
    "Find $(\\sigma , u)$ in $H_{g_N,\\Gamma_N}({\\rm div},\\Omega)\\times L^2(\\Omega)$ s.t. \n",
    "\n",
    "$$ (d^{-1}\\sigma,\\tau) + ({\\rm div} \\tau, u)  = \\langle \\tau \\cdot n, g_D \\rangle_{\\Gamma_D} \\quad \\forall \\tau \\in H_{0,\\Gamma_N}(div,\\Omega)$$\n",
    "\n",
    "$$ (div \\sigma, v)                =  -(f,v) \\quad \\forall v \\in L^2(\\Omega) $$\n",
    " \n",
    " where \n",
    " \n",
    " $$H_{g,\\Gamma}(div,\\Omega) = \\{\\sigma \\in H(div,\\Omega); \\sigma \\cdot n = g  \\text{ on } \\Gamma \\subset \\partial\\Omega \\}.$$\n",
    "\n",
    " The unknown $\\sigma = d\\nabla u$ is approximated using the lowest order Brezzi-Douglas-Marini element (BDM1) and $u$ by piecewise constant element (P0).\n",
    "\n",
    "**References**\n",
    "\n",
    "\n",
    "**Subroutines**:\n",
    "\n",
    "    - PoissonBDM1\n",
    "    - squarePoissonBDM1\n",
    "    - mfemPoisson\n",
    "    - PoissonBDM1mfemrate\n",
    "    \n",
    "The method is implemented in `PoissonBDM1` subroutine and tested in `squarePoissonBDM1`. Together with other elements (BDM1), `mfemPoisson` provides a concise interface to solve Poisson equation in mixed formulation. The RT0-P0 element is tested in `PoissonBDM1mfemrate`. This doc is based on `PoissonBDM1mfemrate`.    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BDM1 Linear H(div) Element in 2D\n",
    "\n",
    "We explain degree of freedoms and basis functions for Brezzi-Douglas-Marini element (BDM1) element on a triangle. \n",
    "\n",
    "### Asecond orientation\n",
    "The dofs and basis depends on the orientation of the mesh. We shall use the asecond orientation, i.e., `elem(t,1)< elem(t,2)< elem(t,3)` not the positive orientation. Given an `elem`, the asecond orientation can be constructed by \n",
    "\n",
    "        [elem,bdFlag] = sortelem(elem,bdFlag);  % ascend ordering\n",
    "        \n",
    "Note that `bdFlag` should be sorted as well. \n",
    "\n",
    "The local edge is also asecond `[2 3; 1 3; 1 2]` so that the local orientation is consistent with the global one and thus no need to deal with the sign difference when the positive oritentation is used. Read [Simplicial complex in two dimensions](../mesh/scdoc.html) for more discussion of indexing, ordering and orientation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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1RE3+WtaAjszPX37o+hnX7N271+FwRGZCwLa4hmQdgRoF7keoK69XS6tjP03KVnInKdc4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\n/g+ot56I1Z+fMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "node = [1,0; 1,1; 0,0];\n",
    "elem = [1 2 3];\n",
    "edge = [2 3; 1 3; 1 2];\n",
    "figure;\n",
    "subplot(1,2,1)\n",
    "showmesh(node,elem);\n",
    "findnode(node);\n",
    "findedge(node,edge,'all','rotvec');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local bases of BDM1 element\n",
    "\n",
    "Suppose `[i,j]` is the k-th edge. The two dimensional curl is a rotated graident defined as $\\nabla^{\\bot} f = (-\\partial_y f, \\partial _x f).$ For RT0, the basis of this edge along with its divergence are given by\n",
    "\n",
    "$$ \\phi_k = \\lambda_i \\nabla^{\\bot} \\lambda_j - \\lambda_j \\nabla^{\\bot} \\lambda_i. $$\n",
    "\n",
    "For BDM1, one more basis is added on this edge\n",
    "\n",
    "$$ \\psi_k = \\lambda_i \\nabla^{\\bot} \\lambda_j + \\lambda_j \\nabla^{\\bot} \\lambda_i. $$\n",
    "\n",
    "\n",
    "Inside one triangular, the 6 bases corresponding to 3 local edges [2 3; 1\n",
    "3; 1 2] are:\n",
    "\n",
    "$$ \\phi_1 = \\lambda_2 \\nabla^{\\bot} \\lambda_3 - \\lambda_3 \\nabla^{\\bot} \\lambda_2, \\quad  \\psi_1 = \\lambda_2 \\nabla^{\\bot} \\lambda_3 + \\lambda_3 \\nabla^{\\bot} \\lambda_2.$$ \n",
    "\n",
    "$$ \\phi_2 = \\lambda_1 \\nabla^{\\bot} \\lambda_3 - \\lambda_3 \\nabla^{\\bot} \\lambda_1, \\quad  \\psi_2 = \\lambda_1 \\nabla^{\\bot} \\lambda_3 + \\lambda_3 \\nabla^{\\bot} \\lambda_1. $$\n",
    "\n",
    "$$ \\phi_3 = \\lambda_1 \\nabla^{\\bot} \\lambda_2 - \\lambda_2 \\nabla^{\\bot} \\lambda_1, \\quad  \\psi_3 = \\lambda_1 \\nabla^{\\bot} \\lambda_2 + \\lambda_2 \\nabla^{\\bot} \\lambda_1. $$\n",
    "\n",
    "\n",
    "Inside one triangle, we order the local bases in the following way: \n",
    "\n",
    "$$\\{\\phi_1,~\\,\\phi_2,~\\,\\phi_3,~\\,\\psi_1,~\\,\\psi_2,~\\, \\psi_3.\\}$$\n",
    "\n",
    "Note that $RT_0 \\subset BDM_1$, and $\\{ \\phi_1,~\\,\\phi_2,~\\,\\phi_3 \\}$ is the local bases for $RT_0$.\n",
    "\n",
    "The first 3 dual bases are the line integral over orientated edges\n",
    "\n",
    "$$d_i^{\\phi}(u) = \\int_{e_i} u \\cdot n_i \\, ds,$$\n",
    "\n",
    "and the second 3 dual bases are\n",
    "\n",
    "$$d_{ij}^{\\psi}(u) = 3 \\int_{e_{i, j}} \\boldsymbol{u} \\cdot \\boldsymbol{n}_{i, j}\\left(\\lambda_{i}-\\lambda_{j}\\right) \\, ds,$$\n",
    "\n",
    "where $n_i = t_i^{\\bot}$ is the rotation of the unit tangential vector of $e_i$ by $90^{\\deg}$ counterclockwise.\n",
    "\n",
    "It is straightforward to verify the \"orthogonality\":\n",
    "$$d^{\\phi}(\\psi) = 0, \\quad d^{\\psi}(\\phi) = 0, \\quad d_i^{\\phi}(\\phi_j) = \\delta_{ij}, \\quad  d_i^{\\psi}(\\psi_j) = \\delta_{ij}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local to global index map\n",
    "\n",
    "Three local edges are `locEdge = [2 3; 1 3; 1 2]`. The pointer from the local to global index can be constructured by\n",
    "\n",
    "    [elem2edge,edge] = dofedge(elem);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "elem2edge =\n",
      "\n",
      "  8�3 uint32 matrix\n",
      "\n",
      "    8    3    2\n",
      "   11    6    5\n",
      "   15   10    9\n",
      "   16   13   12\n",
      "    5    3    1\n",
      "    7    6    4\n",
      "   12   10    8\n",
      "   14   13   11\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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3RKpbotoUptMeZiLVLQ2BoU7dIjN0Q8X+Y1t7erSdXe39PuUuGVXX1VPHy7q6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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "[node,elem] = squaremesh([0 1 0 1], 0.5);\n",
    "bdFlag = setboundary(node,elem,'Dirichlet');\n",
    "[elem,bdFlag] = sortelem(elem,bdFlag);\n",
    "showmesh(node,elem);\n",
    "findnode(node);\n",
    "findelem(node,elem);\n",
    "[elem2edge,edge] = dofedge(elem);\n",
    "findedge(node,edge,'all','rotvec');\n",
    "display(elem2edge);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assembling the matrix equation\n",
    "\n",
    "We discuss several issues in the assembling.\n",
    "\n",
    "### Mass matrix\n",
    "\n",
    "The mass matrix can be computed by\n",
    "\n",
    "    M = getmassmatvec(elem2edge,area,Dlambda,'BDM1');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### divergence matrix\n",
    "\n",
    "The ascend ordering orientation is not consistent with the induced orientation. The second edge would be `[3 1]` for the consistent orientation. So `[1 -1 1]` is used in the construction of div operator.\n",
    "\n",
    "For triangle t, the basis for the constant function space is $p = 1$, the characteristic function. So in the computation of divergence operator, `elemSign` should be used to correct the sign. In the output of `gradbasis`, `-Dlambda` is always the outwards normal direction. The signed area could be negative but in the ouput, `area` is the absolute value (for the easy of integration on elements) and `elemSign` is used to record elements with negative area.\n",
    "\n",
    "Note that $\\nabla \\cdot \\psi = 0$ as $\\psi = \\nabla^{\\bot} (\\lambda_i\\lambda_j)$ and $\\nabla \\cdot \\nabla^{\\bot} v = 0$. So it is simply a zero extension of that for RT0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Columns 1 through 13\n",
      "\n",
      "     0     1    -1     0     0     0     0     1     0     0     0     0     0\n",
      "     0     0     0     0     1    -1     0     0     0     0     1     0     0\n",
      "     0     0     0     0     0     0     0     0     1    -1     0     0     0\n",
      "     0     0     0     0     0     0     0     0     0     0     0     1    -1\n",
      "    -1     0     1     0    -1     0     0     0     0     0     0     0     0\n",
      "     0     0     0    -1     0     1    -1     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0     0    -1     0     1     0    -1     0\n",
      "     0     0     0     0     0     0     0     0     0     0    -1     0     1\n",
      "\n",
      "  Columns 14 through 26\n",
      "\n",
      "     0     0     0     0     0     0     0     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0     0     0     0     0     0     0     0\n",
      "     0     1     0     0     0     0     0     0     0     0     0     0     0\n",
      "     0     0     1     0     0     0     0     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0     0     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0     0     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0     0     0     0     0     0     0     0\n",
      "    -1     0     0     0     0     0     0     0     0     0     0     0     0\n",
      "\n",
      "  Columns 27 through 32\n",
      "\n",
      "     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0\n",
      "     0     0     0     0     0     0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "[Dlambda,area,elemSign] = gradbasis(node,elem);\n",
    "B = icdmat(double(elem2edge),elemSign*[1 -1 1]);\n",
    "NT = size(elem,1); \n",
    "NE = double(max(elem2edge(:)));\n",
    "B = [B sparse(NT,NE)];\n",
    "disp(full(B));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boundary edges\n",
    "Direction of boundary edges may not be the outwards normal direction of the domain since now `elem` is ascend orientation. `edgeSign` is introduced to record this inconsistency.\n",
    "\n",
    "        edgeSign = ones(NE,1);\n",
    "        idx = (bdFlag(:,1) ~= 0) & (elemSign == -1); % first edge is on boundary\n",
    "        edgeSign(elem2edge(idx,1)) = -1;\n",
    "        idx = (bdFlag(:,2) ~= 0) & (elemSign == 1);  % second edge is on boundary\n",
    "        edgeSign(elem2edge(idx,2)) = -1;\n",
    "        idx = (bdFlag(:,3) ~= 0) & (elemSign == -1); % third edge is on boundary\n",
    "        edgeSign(elem2edge(idx,3)) = -1;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Examples\n",
    "\n",
    "### Mixed boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%% Setting\n",
    "[node,elem] = squaremesh([0,1,0,1],0.25); \n",
    "mesh = struct('node',node,'elem',elem);\n",
    "option.L0 = 1;\n",
    "option.maxIt = 4;\n",
    "option.printlevel = 1;\n",
    "option.elemType = 'BDM1';\n",
    "pde = sincosNeumanndata;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:      544,  #nnz:     3424, V-cycle:  1, iter: 15,   err = 5.39e-09,   time = 0.76 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:     2112,  #nnz:    13760, V-cycle:  1, iter: 15,   err = 9.27e-09,   time = 0.22 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:     8320,  #nnz:    55168, V-cycle:  1, iter: 16,   err = 3.40e-09,   time = 0.51 s\n",
      "Uzawa-type MultiGrid Preconditioned PCG \n",
      "#dof:    33024,  #nnz:   220928, V-cycle:  1, iter: 16,   err = 6.30e-09,   time =  1.9 s\n",
      "\n",
      " #Dof       h       ||u-u_h||    ||u_I-u_h||  ||sigma-sigma_h||||sigma-sigma_h||_{div}\n",
      "\n",
      "  544   1.25e-01   1.33049e-01   4.89559e-02   3.51719e-01   1.01710e+01\n",
      " 2112   6.25e-02   6.57965e-02   1.29683e-02   9.19906e-02   5.14701e+00\n",
      " 8320   3.12e-02   3.27711e-02   3.29179e-03   2.32976e-02   2.58126e+00\n",
      "33024   1.56e-02   1.63683e-02   8.26133e-04   5.84713e-03   1.29160e+00\n",
      "\n",
      " #Dof   Assemble     Solve      Error      Mesh    \n",
      "\n",
      "  544   3.00e-01   7.60e-01   2.40e-01   5.00e-02\n",
      " 2112   1.40e-01   2.20e-01   1.30e-01   0.00e+00\n",
      " 8320   9.00e-02   5.10e-01   6.00e-02   0.00e+00\n",
      "33024   2.00e-01   1.91e+00   1.60e-01   3.00e-02\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
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xIz52cHBoamqytbXt3r07vY7hbhmifZsfeIojEAj0nNzA8h1gKmA/jLW0ZZ5u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\nA1GRXUdTutbjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7MrKEHw4IGtFJz80hQoKQUGnFNf+vg7WHN2ONAgmJGIZRKBR8TVLLmX6P5cU8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\n09NuyF+a/MKjusyZgQzfGsz/b6Tk0H986bC1XNv/+2+XJW9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AIAEApEAgAQCkQCABAKRA\nIAEApEAgAQCkQCABAKRAIAEApPD/YwHzNYOXsgEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Mix Dirichlet and Neumann boundary condition.\n",
    "option.solver = 'uzawapcg';\n",
    "mesh.bdFlag = setboundary(node,elem,'Dirichlet','~(x==0)','Neumann','x==0');\n",
    "mfemPoisson(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pure Neumann boundary condition\n",
    "\n",
    "In mixed formulation，the Neumann boundary condition for $d\\nabla u$ becomes the Dirichlet boundary condiiton for $\\sigma$. The space for $u$ is $L^2_0$ and thus one dof should be removed to have a non-singular system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangular Preconditioner Preconditioned GMRES \n",
      "#dof:      544,  #nnz:     3047, V-cycle:  1, iter: 25,   err = 9.64e-09,   time = 0.17 s\n",
      "Triangular Preconditioner Preconditioned GMRES \n",
      "#dof:     2112,  #nnz:    12999, V-cycle:  1, iter: 26,   err = 6.74e-09,   time = 0.07 s\n",
      "Triangular Preconditioner Preconditioned GMRES \n",
      "#dof:     8320,  #nnz:    53639, V-cycle:  1, iter: 26,   err = 6.36e-09,   time =  0.2 s\n",
      "Triangular Preconditioner Preconditioned GMRES \n",
      "#dof:    33024,  #nnz:   217863, V-cycle:  1, iter: 25,   err = 7.62e-09,   time = 0.47 s\n",
      "\n",
      " #Dof       h       ||u-u_h||    ||u_I-u_h||  ||sigma-sigma_h||||sigma-sigma_h||_{div}\n",
      "\n",
      "  544   1.25e-01   1.37562e-01   6.14647e-02   3.94535e-01   1.01710e+01\n",
      " 2112   6.25e-02   6.59922e-02   1.46240e-02   1.02001e-01   5.14701e+00\n",
      " 8320   3.12e-02   3.27830e-02   3.60849e-03   2.57227e-02   2.58126e+00\n",
      "33024   1.56e-02   1.63694e-02   8.99021e-04   6.44489e-03   1.29160e+00\n",
      "\n",
      " #Dof   Assemble     Solve      Error      Mesh    \n",
      "\n",
      "  544   1.00e-02   1.70e-01   1.00e-02   0.00e+00\n",
      " 2112   1.00e-02   7.00e-02   2.00e-02   0.00e+00\n",
      " 8320   3.00e-02   2.00e-01   3.00e-02   1.00e-02\n",
      "33024   1.60e-01   4.70e-01   1.20e-01   1.00e-02\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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chRVBpFrvqK0yu2aiIwUGy3uIjSskloyQCLBSoRwfCGLf0QfLH1SS2MZVWCNq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\nPPj666+rVpVkMpkuLi7kzkYY3pTn7oiMcEdIy5YtCwwMPHv2rPLChNr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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "option.plotflag = 0;\n",
    "option.solver = 'tri';\n",
    "mesh.bdFlag = setboundary(node,elem,'Neumann');\n",
    "mfemPoisson(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pure Dirichlet boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangular Preconditioner Preconditioned GMRES \n",
      "#dof:      544,  #nnz:     3552, V-cycle:  1, iter: 33,   err = 6.58e-09,   time = 0.09 s\n",
      "Triangular Preconditioner Preconditioned GMRES \n",
      "#dof:     2112,  #nnz:    14016, V-cycle:  1, iter: 32,   err = 6.14e-09,   time =  0.1 s\n",
      "Triangular Preconditioner Preconditioned GMRES \n",
      "#dof:     8320,  #nnz:    55680, V-cycle:  1, iter: 30,   err = 9.05e-09,   time = 0.32 s\n",
      "Triangular Preconditioner Preconditioned GMRES \n",
      "#dof:    33024,  #nnz:   221952, V-cycle:  1, iter: 29,   err = 7.69e-09,   time = 0.56 s\n",
      "\n",
      " #Dof       h       ||u-u_h||    ||u_I-u_h||  ||sigma-sigma_h||||sigma-sigma_h||_{div}\n",
      "\n",
      "  544   1.25e-01   1.31849e-01   4.45750e-02   3.42158e-01   1.01710e+01\n",
      " 2112   6.25e-02   6.56419e-02   1.19208e-02   8.96275e-02   5.14701e+00\n",
      " 8320   3.12e-02   3.27516e-02   3.03288e-03   2.27060e-02   2.58126e+00\n",
      "33024   1.56e-02   1.63659e-02   7.61593e-04   5.69922e-03   1.29160e+00\n",
      "\n",
      " #Dof   Assemble     Solve      Error      Mesh    \n",
      "\n",
      "  544   1.00e-02   9.00e-02   1.00e-02   1.00e-02\n",
      " 2112   2.00e-02   1.00e-01   2.00e-02   0.00e+00\n",
      " 8320   6.00e-02   3.20e-01   6.00e-02   0.00e+00\n",
      "33024   1.60e-01   5.60e-01   1.50e-01   1.00e-02\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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C7SCnA2A2GAn7BkyBpvB08wDJVa0VPMXBUyVjrAje8ASRDgAAAPpgXwZJf28G\nNcWRyWRGuu/UIx1kMplh0gATYUtuLgCwYiwdd24+DAvAVygUIpHI+K1F9I1KCCHYqMQ2WL4/Q09s\ndXsKoIKtPmj7miEZAK46YXyeOoh0AAAA0A4YJL1gJEMdRDoAAABoAQySucGRDrjCGI50EIvFllYK\nAADA8oBBMhAjIx3oxWdx3IRcLmdINQAAAKsEDJIhKJVKgUBgpMNNJaeDWCwG9x1gPBAxCLQKbIy1\nWfBqELM5HbD7DiIdACOBjbH6UFNTc+3atVaLQWCqq6uvXbtWXV2ts9FagI2xrIPBH4/YJjGV04Eq\nIEaPdODz+RwOh8HcIYAmYFZhV+zcudPX1/fdd98lCOLf//63eofPP/88ICBg5syZ3bp127hxo5ZG\ngGEsHXduPkwUgK9QKKjqfEbKoddTl0ql2JtHEARTqgJaYPn+DD2x1e0pDPLo0aP27dv/9ttvJEmW\nlJS4u7v/8ssv9A4nTpzw8PDANY1u3Ljh6uqam5vbaqNF9MfY6oO2rxmSKaCmOMa77+iRDlKpFHx3\nAMA4J0+e9Pf3xzVkfXx8Jk6c+PPPP9M7ZGZmjh49Gtc06tu379ChQ48dO9Zqo0X0t23AIDGDSCTC\nEQrGVPyjCqurwG/BcP0AAEAIIXTv3j1/f3/qpb+/f0lJCb2Dm5vbnTt38DFJksXFxXfu3Gm10Ww6\n2w9gkBgDRygwLlZJg3HhAGAtKBSKS5cuGV9Vr6GhgV542sHBob6+nt7h7bffvnLlytKlS7OysubN\nm/f06dOamppWG43UBFAHDBLrIFqwtCIAYHnq6urmzZvH4/F69OgRHBzs5uYWHR2Ng4m04+zsvG3b\nNvV2FxeX58+fUy+fP3/evn17egdfX9/MzMzCwsKlS5f27t37jTfe8PLyarXR+LsDVACDZFoMiL5T\ntKBuk2CjEmBX1NTUhIeH79ixY/Xq1YWFhYWFhevXr8/Ozo6MjHz06JFhMgmCyM/Pp17m5eWp/KE9\nfvy4qalpz549crl8wYIFly9f7tevX6uNxtwa0DqWjqowHxYJL0EIEQShUCgMOJf6O6EiHVCLY5Bh\nLQHWRx/piY0FX61evbpdu3YXL16kN+7btw8htGLFCu3nOjk5bd26Vb396dOnnTt3/uabb0iSPH/+\nvJOT05kzZ0iS3Lhx46lTp0iSrKysdHd3v3TpEkmSx44dc3V1ra6ubrWRobs0BBt70BRgkEwLDuY2\nrHoFPeybPmEyvhYGoA7L/1D1xJa+p5qbmz08PGJiYtTfWrNmTVpamvbTnZyckpKSZs2axePxPDw8\n4uLiqqqq8FuHDx/u2rWrp6ens7PzF198gRu7du26dOlSfLxly5bAwMBu3br5QrtaSQAAIABJREFU\n+vriAHFNjZbClh40HTBIJofaqCQQCAybKqnIocySMdIAFVj+h6ontvQ9de/ePYSQTCYz7HQnJycf\nH5/x48fv2LEjISHByclpyZIl1LvNzc0lJSX19fVaJDx8+FDPRvNjSw+ajn2tIVlkQz6V08HIehMq\nxWehegWD2FKmBpu5l4KCAoRQ9+7dDZZAEMTRo0fffffdNWvWjBs3Lj09nXqLw+H4+Pg4OjpqOb1r\n1656NloFVpHLzkF3FxvCgmm+8NpPWloatigGF1iSSCRxcXFisVgul+P0d8ZIAzDx8fEpKSmW1oIZ\nGBnkDWV3tbzr6Omv0sJUf/WeKjHZbWLSpEnUcXBw8JUrVwwWZQPEx8fHx8ez3CbZl0GyLNS+V6lU\naowJwTkdKNsmlUplMhlV9w8AjKdKvvfx3rWa3u29r0SlRTEnVIs0/fu7xyS4xyTgY7wTvNX9p7t2\n7SopKUlISNByUfTybIbD4ZAkqb0/YHHAIJkbPMUxUgi2bXFxcUKhEO+ZFQqFxtdZBwCMqyDGVRCj\nf3/+puw2ydfUnz5D8vPz4/F4hw4deu+991S6rVixguW/9AHDAINkAZiaytDdgNh9B1MlgBHUXWfm\n78/lcufPn//pp5+ePn16+PDhVHt6enpOTs6CBQvadEXAKrCvoAbbAyIdABtmwYIFPXv2jIyM/Pbb\nbwsKCh4+fPjDDz/ExMQMGzZMLBbTe1ZVVRUVFVlKT4ApwCCxAg6HY3zxWVy9Ak+VwCYBNgCPxzt/\n/vwbb7yRkJDQq1cvT0/PmTNnvvXWW0eOHOFyX/ruSkxM/PTTTy2lJ8AYlo47Nx9sDsDHUxwjtxbB\nRiVjYPPw0B9b3Z7S1NSUm5ubk5NTU1Oj8tYnn3wSHh6OEIqLi7OEapbBVh80zJBYAZ7iEARh/EYl\nKqcDuO8Am4HL5fbr12/AgAEuLi4qb40ZM+aTTz4RiUSW0AtgGDBIbAEHc4tEIqlUimPnDJaTkZGB\np0rYfWdM2UAAYDn/93//N3bs2F69ellaEYABwCCxCMjpAACAPWNfBskqsqrgKQ6eKhkf6UC57yDS\nQQtWMTAAwOaxL4NkwdRBbYKa4hi50ZXuvkMIgftOE9YyMADAtrEvg2RdMJJ2ASIdAACwFmzfICUe\nV8gLK/hfZOVP2Mz/IkteWJF4XHf9YxsDIh0AAGA/Np46SLz7huxcKXHeRVlei1uEmy7hA8lYvuX0\nMhA+ny+RSAyLcKWndkUtUyVIfwfYBkuXLrW0CgAD2PgMSRLFRwhR1og6GBXYxWI6GYpSqRSJRGKx\nGCIdAC1AgAbQKlZRD8nGDZJw80X1RsLNRbz7hvmVMRIq0sFIhxtEOtg2EKABtEp8fHxeXp6ltdCB\njRskakqk0thqu1WApzgIIcjpAACAjWHjBolwU000ghtbbbcW6BuVhEKhkXIg0gEAAJZg4wYpNbZf\nm9qtBXpOBz6fL5fLjZEDOR0AAGADNm6QThZUqjdatcuODjVVwoUnDAYiHQAAYAM2bpAkY/nSKH7G\nnNdUfHS3bcIgIVowt/FyINIBYBt1dXVNTU3qx2yAzbpZLzZukBBCkrF8QU+eYllY76OzFcvCcKPs\nfKm8sMKyirENiHQA2Mbo0aMPHz6sfswG2Kyb9WL7BokO4eaCV4+U5bXWGPmtJyrVnduEeqSDMbUw\nAAAwEbax7qCCfRmk5ORkUYiPKMQH2bRNksvlDEY6yOVym58qwWZSwOoQbr4o3n3Dxjw99mWQ8J5B\nSRQfLynJzpXaZF47HOkAOR30BzaTAlaHsrxWdq5UuOmScNNFmzFL9mWQMISbS8bsYHxsk4tJeIqD\nNypBTgcAsEkEPV/kP5MXVgo3XeJ/kSU7V2pZlYzHHg0Sso/FJAZzOmRkZECkA6CdxMRE7CvmcDjY\nYwzjxKRkzAlOje1HmSX8Vcb/IsuqvT52apAQQqIQH/wsbdgmMVV8ViAQQKQDoAWxWCyVSsViMTUq\nhEKhSd28paWlYrHYy8vLtQUvL6/m5mY2SDMbohCfjDnBimVheF0cIaQsr5WeUFivWbJfg4QQSo19\nlVpMsoHZbqtQwdwymcx4OXYV6QDoD94MR1kj6mDUqFGmuFxRUZFQKIyKilIoFAkJCUFBQY8ePbp3\n7x6X+9IX2uPHj9No3Lx50xhprAX7exTLwqRRL0rq0M0SPRiPKgtnIU11Yx2fuImgHHcIocQTCpsM\no8TgqZLxcuwq0gHQn1ZzKhIEYcwOBC3MmDFj5cqV06ZN69Chw0cffZSdne3k5OTgoFrdDVdsofj1\n11+NkcZyCDcXyVi+ulmyrmA8K/vQGUfQkyeN4ktPKJTltcLNF6mds7YHtiKMyMnIyEhLS8OzJalU\nKpPJqEUmwDaQyWRt+qnRqv8WN/L5baiEqU/FyHPnzt25c2fSpEn4ZXFxsZOTU6s9Bw8eTJIkU9Ks\nAmyW4kJ80s6Vys6X4jRpsvJS2blSarWJzdi7QUIIxYX4yAsr5IWVeDHJ2vOumgHsvhs1ahReM1Ap\nPosj8QiCwCEVgDVy+/ZtptYIGV9rzM/PHzFiBPXy8OHDM2bMYIk0lkCZJXlhRdq5UnlhJUII/4+h\nvHZs+wkOBgk77l4Vbr6I4/rjQrwFPXmWVsoccDgcqVRqcCo8HOmAp0rYfSeXy1NTU5lVErAIAQEB\nbZryarI6ppg3d+vWjUocV1FRsX379iNHjphIWnV1dXZ29ujRo41R2FIQbi4iNx9RiA8n4Td6O5vX\nJsAgIdSymCTcdAkhJN59I2N2sFUXTNKTjIwMsVgsk8lSU1MNyxdOpXbF7jsc6QDRdzYAXnTRv39i\nYiIV8EIH74djSKkXjBo16j//+U9qaiqPxzt06NDOnTv9/PxMJO327dtTpkypqLCOBRhNUN9mlCli\n7febHRmk0bwGLe/SF5PEu3Mz5gSbTTFLQU1xxGKxPr57TUgkkri4OLxUQLdG1OIB+O5sHjx4KC8u\nXmiUy+WMWyPM999///Dhw+bmZmrthz3SWAjll+N/kaUsryXcXNjmqaOwlyi7hrK7C7vVPt67Vkuf\nuJadSfLCSiuN4m8rDOZ0UGlR0jBOR8A6kEgkAoFAoVCQJIlDMU1kjTAeHh5eXl7mkbZu3TovLy93\nd/f58+czdUXjuZ+y8Pl19gZwG4a9GCRHT/9dD5yqMvZqeYR4MQkf22RKIU0wldMBo95unHbAn+zZ\ns2fChAkTJkzYtGmTpXWxF6qqqnJzc3Nzc//3v/99//33p06dsrRGL2h4eLdYMkUxO9SmzBJpN4wY\nEHhneXTRB0O1d0s9W4IWpaNF6cTnfyge15hHNzagUCioSG5j5KhYIOpXM8vp3bu3pVXQQX5+fkRE\nREVFxfPnz6Ojo0+dOqXex+C7YOftHzhwoKioSP3YbFy7do3D4VRVVeGXo0eP3rZtGxt0w8+r/sGd\nO8uj8yb76PxaUzmRtdjLDAkhVFbP9Z67vuHh3fspC7V0E4X44J1leDHJXNpZHiptHSMlaCkgpwNT\nnD59esyYMV26dGnfvv0bb7yRmZlpaY1MzqRJk6iVSPqxOXF1de3UqRM+dnZ2bmxsZI9ujp7+/ok/\n8jdlt+8/3PxXNwV2ZJAQQo6e/t5z11fJtTnukF0uJlEYFm6nDt6HBDkdGOTRo0ceHh74uGvXro8f\nP7asPnYCh8OxtAo6cPT095633tJaMIN9GSSEkKswxlUQ8yDlnw1ldzX1sdvFJEagL2tD9Qo9qa6u\nvnv3pQFZW1t769atqqoqqoWkJR3A/g3z6QdYIdYY9WBfBgkXBnWPSUAI3d+ozXFnD/Up9ITP59t8\n9QqLV4xNSUnZuHEj9fLIkSMjR45cvHixUChcvXo1buzSpcujR4/wcXl5eZcuVpAJBrAUVRl7a66f\nLpZMsTKzZMH1KzNDX82rf3Anb7KPzlNEu3JxgINoV64pVWMvTEU6UHIwLIx0sNRi7/r162NjY3v3\n7r1kyRLcUlFRMXDgwDNnzpAkWVZWNnTo0D/++IMkyYsXL0ZFRTU0NJAk+e677x49elRdWu8WkpKS\n2qQGy9e6ARX0fF5PftuDox5OTfSbHcrHY8PUuhmDfc2QKBw9/XvvK9HZzeaLneuEmuLIZDIjNypB\n9YpWCQsLmzt3bnR0NNVy9uxZb2/v0NBQhJCHh0dERMTvv/+OEHrttddGjhwZGRk5duxYHo/317/+\ntVWBeXl5eXl5UJQdQAi5CmNw1ENg1JSF3WqPRXTxdGJ1kSc7NUh6YvPFzvUE53QQiURGWhGoXqFO\nSEjIiBEjAgICqJYHDx74+PhQL729vcvKyvDxxx9//PPPP+/fvz8pKaldu3bm1hWwTnDUA39TtntM\nQlk9q7/zWa0cG4DFJAyDOR0g0kE7jY2NdGPj4ODQ0PBn1isXF5eOHTtaQi/AunH09HcVxlhaCx2A\nQdKNPRQ71xOmcjpYRaSDpXB2dq6t/TMfc01NjbOzswX1AQCzAQbpBVqiwJF9FDvXEzzFMSYZKwa7\nAfFUCbvvIFM4xs/Pj/45KBSKbt266X+6xSMGAXaSnJzcp08fS2uhAzBIqKHsrmJ2qJ5R4MjWi53r\nA1V1ghE5EOmgQkhISF1d3e7duxFC169fP3nyZKsFwjUB4Qz6UFNTc+3atcrKSt1dbYX4+Pi8vDxL\na6EDMEjI0dO/W+K+muuntecCx/UpEEK42Lm5tLN9INJBhQ4dOqxatWr9+vVhYWGxsbHz5s0bNGiQ\npZWyKTZt2uTr6xsXF0cQxCeffGJpdQAalo47Nx/aA/Af7VlT9MHQZ9f+0NJH8bhGsPGCne9M0gTO\nFWTw6SoblYyUZgBs25/R3NxcVlaGdx3pj40lVzUFOTk5r7zySn5+PkmSSqWyc+fOmZmZllaqzdjq\ng4YZ0gtcBTEOnt0epPxTSx+cUohaTLLbKHBNQKQDg3A4HA8PDweHNpfQhDUk7Vy9enXMmDG9evVC\nCAUEBAQGBhYUFFhaKXNgFWtIMEP6E5y+oTR5gfZuGQXl9lmfQjvWntOB5b8c9cRWfzibiLy8vPbt\n29+4ccPSirQZW33QMEP6Ez1zgdMXk+yqPoV2IKcDYFIUCsWlS5cYDEPIzMyMiIhYtmxZ3759mZIJ\nGAkYpJfQJxc4su/6FNrBwdwCgQByOgCMUFdXN2/ePB6P16NHj+DgYDc3t+joaLwZTjvOzs7btm1r\n9a36+vpFixZNnTo1KSlp2bJlTKsMGA4YJFX0zgUO9SlahyCI1NRUyOkAGE9NTU14ePiOHTtWr15d\nWFhYWFi4fv367OzsyMhIKvG5AUyePFmpVF6/fp2eQhBgBZb2GZoPxp2ndlvsXE/wFMd4OVSkA0KI\nIAgj16g0wXLfup7Y2NLC6tWr27Vrd/HiRXrjvn37EEIrVqzQfq6Tk9PWrVvV2w8cODBgwIDGxkYm\nFTU7NvagKWCGZDh2W+xcT/AUx3g5kNOhTdhMlB1JkqtWrZo8efJrr71Gb588efKaNWt8fX11Snj2\n7NkHH3zg5ubm6ekpEomePn2KEPrll19yc3M7dOjg3ML+/ftNdQ9sAqLs2IUpfhrQdyZJjxUxLh+g\no7JRidmpEst/OeqJLf1wvnfvHkJIJpMZdrqTk5OPj8/48eN37NiRkJDg5OREVZyyAWzpQdOBGZJR\nwGKSOYFIB7sCbw/q3r27wRIIgjh69Oi77767Zs2acePGpaenM6cdYBLavO3ODnl+PatD/zBN7+I0\nd+LdN3AucMUyjT0BhBCHwxEIBKmpqdSyUJvAbsC0tDRqz5NMJqMvMgGMoN0jqv5pM9VfvWd9fb0W\nydqZNGkSdRwcHHzlyhWDRQHmAQySDh7vXVuVsbdb4j5HT39NfUQhPicLK2XnSrFNotKwAuooFAqh\nUCgUCg3OF443Ko0aNUosFiuVSpzTwfjs4wAdyuS3CkmSKi18Pl+LNP37S6VS6jniPnfu3FHvtmvX\nrpKSkoSEBC0XRQh17dqVOuZwOOpqAGwDDJIOXAUxVRl7729c6J/4o5Zukii+vLBCWV4rO1dK8Fwk\nY7X9fdozKlMcg60IjnTAcrD7Ti6XGzzxAlSIi4uLi4vTv78+G4P06U9/fH5+fjwe79ChQ++9955K\ntxUrVljB+jxgABZewzIjBq/m4ZRCj/as0d5N8biGigLPKCg37Fr2Q2pqKmIiiSpTkQ4sX+zVk969\neyclJRl2IuPKGI9EIuFwOFlZWfTGX3/9FSG0ZcsW7eeqhH1/9tlnjGxCYAkGPK+kpKTevXuz80FT\nQFCDbhw9/d1jEqoydKQUgmLnbUIkEuEIBcjpwCy2VA9pwYIFPXv2jIyM/PbbbwsKCh4+fPjDDz/E\nxMQMGzZMLBZT3eywuJEBQD0k20GfXOAIip23EXpOhzbVoFOXAzkdbBIej3f+/Pk33ngjISGhV69e\nnp6eM2fOfOutt44cOcLlvvjuguJGNoWlp2jmw2BvBkbPXOCKxzXE539g313q2RKDL2dXMJXP2+Cc\nDtibwYgOlsVWt6c0NTXl5ubm5OTU1LyUEsU2ihsZgK0+aPuaIRnjzaBygVdl7NXSDYqdGwBTkQgG\n53SwJTeXTcLlcvv16zdgwAAXFxd6u90WN7JV7MsgGYmrMMY9JkF7pXMExc4tClSvsCumT59+4MAB\nfJyfn5+bmxsaGmpZlQBjAIPUNlwFMfzN2Tq7xdEWk6A+hQHw+XyIdAD0B4ob2QZgkNqGlu2xdOjF\nzqUnFJBSqE0olUoq0gGqV7QVm0muqidQ3EhPrCK5KhgkU0FfTMKJhSyrjxWB3W4KhQJnYTB4ckMV\nsaWmSvbgvrO39TAobqQnEPZt70Cxc2PAUxw8VTLGikD1Chvm4MGDSqXyv//9b5cuXSytC8AAYJCM\n4n6KtsKyCIqdGwcVoWB88VmIdLBJ7La4ka0CBslwqjL26hcFDvUpjIKKUICcDoAKGzdubGpqqqMB\njjurBgyS4VBR4A1ld7V0U0kpBItJBkDldDAypbeWSAeFQsHhcLRnrQYAwKSAQTIKnFLo/kYdjjt6\nsfPEE+C4MwTsdmNKjr1FOgCAVQAGyShw+oaa66d17palFpNk50phMcniqEc6NDQ0WFopALB3wCAZ\ny4uUQnrlAofFJIYxPtKhVZkYozQDAKDtgEFiAFehXrnAoT4F4xgf6aCCkgZTMs2MvW2MBfQENsba\nEd5z1yM9osBFIT6iEB8ENokh6NUrDDMhRAtaWqwLW9oYW1dX19TUpH7MNqxCT9gYa0e8KOIn1xYC\njpFE8XFKIVhMMh6VnA4ymaytEhQtODo6opYKthjm1QXayOjRow8fPqx+zDasRU/2AwaJMVyFMb33\nlejsRri5ZMwOxsewmMQIVE4HsVhsn/FyiYmJcrmcz+fn5+fz+Xy5XG6fnwNg7ThYWgF7BC8m4T1J\n4t03FMvCLK2R1UNFKEilUplMRq/UZ/OIxWKZTEYQBOW0pMrvMhIoDwBmA2ZIlgGKnZsC7L5DBlX8\n4/P5JElao6cOWx3KGlEHo0aNspBGAGAgYJAsBlWfQnauVHau1NLq2AjYfWdpLcwKNR+iQxCEWCw2\nvzIAYAxgkCwGFDs3EfbjrMO0Gl5o1ZHrgN0CBskkNJTdVcwO1RkFDsXOAePRZIAtY5j5CHEQMv2u\n4tLSUrFY7OXl5dqCl5dXc3MzmyUDOgGDZBIcPf295n2tMxc4gmLnZgFnTbXVGUNqamqr7SKRyLyK\nmI+ioiKhUBgVFaVQKBISEoKCgh49enTv3j0uV+MX2uPHj9No3Lx5kynJAIPAp2wqOvQP0zsXOBQ7\nNy04VMFWk6iePHmy1Xa8X9jMypiHGTNmrFy5ctq0aR06dPjoo4+ys7OdnJwcHLTFDCuVShGNX3/9\nlSnJAIPAB21CXAUxz69n3d+40D/xRy3d8GKScNMlhJB4942M2cHYPgFMgSMd0tLSpFKpUqnUNKWw\nUnCU3ahRo8RisVKpxDeLU1fgzUmGBMHLEDLMditbDgzz2okQ0hWpfu7cuTt37kyaNAm/LC4udnJy\n0il48ODBJEmaQjLAIDBDMiH65wKHYuemhsrpgL+j5XK5pTViEolEIhAIFApF7969Fy1ahG0Svb5G\nm92VtxFSGvQPY9i5+umYn58/YsQI6uXhw4dnzJjRppszv2Q2ALnsAH1zgSModm4W7CGnA85lZ6xN\nCkCIMOgfhZGna6Zbt25UsriKiort27cvX76c3iE9Pf3hw4d6yWqL5Orq6vT0dAPEsgTIZQcg1LZc\n4FCfwuTgqRJOyWrbNSYo64sMqEMoQkhh0D8CX9vQ0/XILDFq1KjOnTunpqYePHhw0aJFO3fu9PPz\no3eYMmXKmTNn9P+g9JR8+/btKVOmGCAW0B8wSOZAz1zgUOzcbGD3nTXmZWgT2PpSdQhlMpltzAu/\n//77CRMmDB8+PDU1tW/fvlYhGdAHMEjmwNHTn78523veep096cXO+V9kcRJ+43+RJS+sACce49jJ\n/lkVmySVSm3DJnl4eHh5eZlf8rp167y8vNzd3efPn2+Kq9s5EGXHOpQVqhMjHICHEJKMtWUXE2A6\nqMyz1P+myrtq0z+cqqqqcnNzc3NzCwoKBALB22+/PXLkSEsrZVPADIl1SKJesjqU425UYBdLqANY\nE1VVVZrekkgkVLy7VCq1ikx3ixcv/stf/qJ+bClIkvz666/d3d1DQ0PDw8MLCgrUdWODntYLGCTW\n0WoOIcLNBZKCA9pRKpX379/XEqkhEomoZTOZTMb+mI5JkyZRStKPLYWrq2unTp3wsbOzc2NjIz5m\nm57WCxgky6AlCrzVWAZleS3EOADaIQgCfxVqyZOES+JS4eA2nFHJFHA4HEurYOOAQbIAdyWTtUSB\nt5qmgXBzgfQNgE4cHR1x9Q0tG48Y2DYLAKYBDJIF0B4FTtWk0LMdAF7AR3n5eYSQ0NMmCQQC1GKT\nzKglAGgEDJIF0J4L/GRBpXoj5AIH9IeaAwmFQk1JkgiCSE1NpcLBzaidyamoqJg4cSLjYvv3719R\n8ed29Z9++um9995j/Cp2jmkN0qRJkzZu3GjSS1Bs27btzTffnDBhwpYtW8xzRWPQkgtcMpYvjeJn\nzHmN8tFBSiE2Y85Brj/Y3mhPkkQQRFxcHLZJAMAGTLsPaeTIkadOnZo9e7apq4lkZWX9/PPPu3fv\nbmpqmj59+sCBA4cOHWrSKxoPzgVeLJnC35yt8hbeb6RYFoZf4k2yCCHZ+dJRgV0EPXlmVhXQgtkG\nuUaokC7lSy0EIuIy4pDWLUd42yxCaOfOnSbUEAD0w7R/QjNnzvTx8Zk1a9Yvv/ySk5NzowXGL1Ra\nWjp9+vT27du/8sorQUFBd+9qK0HEEnDe1YaHd3XmAldJKWQW7QB9Mdsg14hSY6Ztyt5ox1SbZAGg\njZh2hvTPf/7z3LlzCKHff/+d3s540tnJkyfjg5KSEvxzlVn5JgLbpMd717bvP7xD/zAtPUUhPicL\nK2XnSrFNggAH9mC2Qa4RouVA2VojAFgPpjVImzZtwnvHmpubu3btWl5erueJ1dXVFRUV/v7+VEtt\nbe3du3dxoXvckpWVdfz4cYRQz549Z86ciRD67bffVq5cKZVKu3XrxvCdmAxXYcwT+Z4HKf9Ud9yp\nIIniywsrlOW1snOlcSHe4LhjCQYPcsagFhb5L9skWHAEaCQnJ6ekpFhaCx2Y1mXn6upaUFAwd+7c\niIiIV199dfr06enp6Tye7m/SlJQU+kLxkSNHRo4cuXjxYqFQuHr1atzo5+c3YsSIESNGDBgwACG0\ncuXKnTt3pqWlRUREmOh2TIR/4o86rRGiOe4QQpALnD0YPMhNi1JjzVYI8kYI1dTUXLt2rbKylYhW\nWwXqIaHLly+LRCJ3d/fExMS1a9eOHDny008/lclkWk7ZsGHDtGnT6EWmKysrP/7445SUlEOHDh07\ndmzfvn1ZWVkIoYCAgMjIyMjIyODg4F9//VWpVH7//fc+Pj4mvSPLAoVlWYgBg9zkEAihFpukfOkd\npVIJCRo2bdrk6+sbFxdHEMQnn3xiaXUAGqQpmTVrlkQiobf89NNPQ4YM0XLK2bNnT5069eGHHy5Z\nsgS3HD9+PCoqiurw4YcfrlixQuWsf//73yNHjhzfQkZGhrrk3i0kJSUZdDesQPG4RrDxAlqUjhal\nS48VWVodqycpKYkaGIZJMGCQm44Xd6EgSYIkEUkikiRIUvFSH5w6COcQUj3RDsjJyXnllVfy8/NJ\nklQqlZ07d87MzLS0Um3G4OfF8gdt2hlSXl7euHHj6C1RUVHPnj27f/++plNCQkJGjBgREBBAtTx4\n8IA+7/H29i4rK1M566uvvvr999+PtoC3oLeqT15eHq7xbKVAYVlmwX4MY1wZBgxyk0MglEGbJwlf\nmifhbbNIayoHG+bq1atjxozp1asXQiggICAwMJBK2g1YHNMaJE9Pz9u3b9Nb7t27hxByc3PTX0hj\nY2O7du2olw4ODg0NDUxpyEIgCty6YGSQMw+BUAZCAoSQRpukPZWDrTJ9+vQDBw7g4/z8/Nzc3NDQ\nUMuqBFCY1iBFRkauXbv25MmTzc3NCKFbt24tWrRo1KhRTk5O+gtxdnaurf1zAb+mpsbZ2Zl5XdlB\nVcbeqoy9WnKBY0QhPjh9A9gki8PIIDcJBEKp2mySzlQOrEKhUFy6dInBMITMzMyIiIhly5ZBqXL2\nYFqD9Le//S0iImLWrFkDBw4MDg6eMGGCg4PDZ5991iYhfn5+dMeCQqGwoqjutuIqjGnff7iWXOAU\nqbGv4txCsnPguLMkjAxyU0EglIqQCCHUuk2Ki4sTiUQWDsHQSl1d3bx583g8Xo8ePYKDg93c3KKj\no6mqTlpwdnbetm1bq2/V19cvWrRo6tSpSUlJy5YtY1plwHBMuw+Jy+V++eWXf//7369du1ZbWxsY\nGDh48OC2CgkJCamrq9u9e3dsbOz169dPnjz5/vvvm0JbluAek1AsmXJ3YpcMAAAgAElEQVQ/ZaH3\nvPVaumHHHa5uLt59I2N2MNSnsAiMDHITQiAkQYhASNpik6hpE+tTB9XU1IwcOfLWrVtr167F2zmO\nHj361VdfRUZGnjlzpmvXroaJnTx5sqOj4/Xr17t0gSrMLMOkIRNvvvlmSkqKASdu3ryZirIjSTI9\nPT00NHT48OEDBgzYvHmzYcpYUXzds2t/5E32efLbHp09pceKcMSdaFeuGRSzVXCsnWHnGjzITYHG\nu1CQpJQWd5eh94kWZfXq1e3atbt48SK9cd++fQgh9VBbFZycnLZu3arefuDAgQEDBjQ2NjKpqNmx\n1Sg70xqkNWvWTJ06tampyXhRzc3NZWVlDQ0NBktg+ZNQ4dGeNUUfDK1/cEd7N4gCZwqDhweDg9x4\nih2L1Y3NCxTabBIL/zqam5s9PDxiYmLU31qzZk1aWpr2052cnJKSkmbNmsXj8Tw8POLi4qqqqkiS\nnDNnDpfLdaLx448/muQGTImtGiQOSZKmm349fPjwyy+/rK6ujomJ8fb2dnB44SHs188Cqdj69OnD\n/o3KFA1ld+9vXNhYVqwziQOVC5xwcwHHncEYPDxYNMiVKHlIcnyneLpTTpVEhKQIIYQIhEQItWRV\nZeFfR0lJiZ+fn0wmi4uLM+B0Z2dnd3f34ODg2NjYy5cvJycn//Of/1y5ciXjeloEg58XCx80HRtJ\nrmp74Lyrijmhj/eudY9J0NITLybhZELCzRepohWAeWDRICfQAdcD8XHxSPySsXkJ3ChFSImQjNbC\nPvD2oO7duxssgSCIo0ePIoTefffdwsLC9PR0xpQDTIOZkqsCBkDlAtdukBBCgp48Qc8u8sJKXFgW\nl1MCzAOrBvk9x3sITydkCCEjbJJS62UIk/VX61lfX69VtDYmTZpEHQcHB1+5csVgUYB5MK1Bmjlz\nZmRk5Ny5c016FRvGVRjjKozR2Q2nb4AifhaBdYOcoJkcpLdNUiGt5fRWUXfza/8JpH9/6Z8K8/l8\nhNCdO3fUe+3ataukpCQhQccPNXoYHodj2uUJgBFMuw8JF9PEGwYBkwLpGywFSwe5BCEpQlKENO15\nlbSYHGVrticOIYXmf+po6dym/jTz6efnx+PxDh06pH72ihUrzpw5o/nmAWvF5DOk4uLiWbNmWX69\nFyGEUHJyslUnstOOKMTndnmt9IQCivi1leTkZIPPZdsg/xP950nqEG28lgn6c7nc+fPnf/rpp6dP\nnx4+fDjVnp6enpOTs2DBgjZeErAC7CuowYatESYuxEd2vhQX8RvVs4soxJaLcTBIfHy8wbXL2DbI\nX0JC+19ThwCExGZSp60sWLDghx9+wMmZRo8e3blz5xMnTsyfP3/YsGFi8Z9KP336VKlUdu/evXPn\nzhbUFjAeCGqwKXDkN15MSjyhEPTkQRS4qWH7INcZRCdCCCG0wtR6GAKPxzt//vzs2bMTEhKePXuG\nEOJyuWKxeOXKlVzui+WGtWvXfv755/7+/gUFBcuXL//www8tqjJgFHa00MfyAHydNJTdVcwJdY9J\n0Bl0l3hcIT2hQAgRbi4QBa4n1j48MLa6PaW5uTkvL6+pqSkwMNDF5c/fWDdu3BgxYsTVq1f9/Pyy\nsrLCw8OLi4v9/PwsqKp5sNUHbZKghj179mRmZuLjpqamoqKipqYm/LKkpASyGRoGjgLXJxd4HC0X\neOJx3WkoAQOAQW5OuFxuv379BgwYQLdGCKHy8vKEhARsgQYOHOjg4EA9BcAaMYlBSk9Pv3r1Kj5+\n/Pjx66+/XlHxIh11RUUFTkUFGICeucChiJ8ZsNZBztcVom1VhIeHL126tKqqSiaTTZw4cf78+cZs\npAUsjmnDvgHGwf66+ykLtXeDKHBbpbq6+s033zT8/AyEEEJ8XVtZrYpnz56dPXu2srKyvLz86dOn\nllYHMBwwSFaGo6e/17yvq+R7dRaWFYX44Cg7sEm2QWNj48qVK6Ojo8vKygyXQrTYJKHt2CQfH59N\nmzZduHDh2rVr7KyjAegJGCTro0P/MPeYBH0WkyRRfKqIn+xcqVm0A0wFl8sdM2YMA6X/CNuxSV9+\n+SW1l4PL5Q4ePDg3N9eyKgHGYF8GyZj9j6zCVRDj4NlNv8WkF9szE08olOW12vvbLVYxMLhc7pAh\nQ4YMGcKALMJGbFL//v23b99+4cIFhFBRUdHhw4dHjhxpaaUAwzHVPqT09PQHDx4ghJ4/f44QWrVq\nVfv27RFC5eXlJrqiPtjMxlgqF7jOwrKCnjxpFL8lfUNuxpxgsylpRRi2MdbIQV5dXV1RUeHv70+1\n1NbW3r1718vLy9XVFbdkZWUdP34cIdSzZ8+ZM2e2VUNtEAhlICRGSNhinKyQN998c968eeHh4Z6e\nnlVVVQsWLJgyZYqllQIMxyQGydfXt6SkBP9sQQj16tWLPo/u1auXKS5qbzh6+vfeV6JPz7gQH3lh\nhbywUl5YCbnAmcL4QZ6SklJZWUlV6Dly5Minn37q6+tbXFwcGxv7r3/9CyHk5+c3YsQIhJC7uzvz\n90AglIpQGkJChJyYF28evvjii8TExAcPHnh7e7dr187S6gBGYRKDJJVKTSEWMAzIBW4KjBnkGzZs\nOHPmzMWLF9966y3cUllZ+fHHH3/33XehoaEPHz6cMGFCeHh4WFhYQEBAQEBAm4T36dMHITRv3jy9\n/AEEelGuwppDARwcHOxhM6zBJCcnG5wZy8zY1xqS3QJR4KwiLCxs7ty50dHRVMvZs2e9vb1DQ0MR\nQh4eHhERESqZ8fQnLy8vLy+vDd5pgr01+gBGiI+Pz2vB0rroAAySvQBR4OwhJCRkxIgR9KnPgwcP\nfHz+zITr7e2tKba7Xbt2p0+fNrmKAGAJwCDZDm2KAof0DayisbGRvv7h4ODQ0NBgQX0AwCKYNts3\nYB4ayu7e37iwsayYvzlbSzfsuBNuuoQQEu++kTE7GHKBswRnZ+fa2j+D8mtqapydnc2pwNChQ/Hi\nE2AVDB061NIqmAQwSLYARIFbO35+fkqlknqpUCgMDkY1rArljh07/nyR2FJtttW1JSWtwDmBUCpC\nAo1ilUolQRDq7RwOR9Mp9lN/wMxYRWiDfRkk01WMnTFjxtmzZ00huS10Qjk/o+SfdfbrjRBCqASh\nPhtMrRKTDB069KXvTeaw+MbYkJCQurq63bt3x8bGXr9+/eTJk++//75hohgY4fSqfeo2iWgJzJMi\npERIrNEm8fl8hFBGRoa6TSIIgm6A6e0G6gzoIj4+Pj4+nu3zYNJu6N27t5UKBzA29gQ3b968ZMkS\n6mV6enpoaOjw4cMHDBiwefNmw2QyeRepJIlIUqThXQVJSkkSkSQiSYIkM1rrolAQBEEQhEKhUHkr\nI6P1vbitdgYYhOXfVPY1QwIA9vDBBx/QX0ZERJw+ffrRo0c8Hs/BgQV/mCKEBC21KlLV3iVaJk/S\nlnmSSHU6RRBERkZGYmKiUCiUSCQikYh66+TJk61eU6lUCoXCVidVgD0AUXYAwBY4HI6Hh4eR1ohJ\n9yOBkAIhmeYSSpKWxSQlQjKEEtUEEAQ2RYmJiYmJf74tkUikUillePDECFssbJNkMhljdwEghBBK\nTk5mu78OgcvOGoQDGHiCOjHJXShIkiBJQnMHuu9OqqGLVEoQhFSq4W18HYWCyn+hszNgGCwf5yzw\nDAAmo66uzsHBAW9woR/bmw6AURAIZSBEaO5A993JaC30LhIJasm3hI9buQ5BUN2USiWeJGnqDNgk\n4LKzZUaPHn348GH1Y3vTATAWQlcHuu9O2orvDrW46XTmAMTdEEJKpVIqldIdfYDNAwYJAAAmoGwS\n0maTSD22GVE2CSEENsmuAIMEAABDSGjxeNLWbZK+kiSS1NQXsqRSqVgsNlI1wCoAgwQANoWZNvny\nEZK31i5izCaJRCKFQoGPZTKZUCg0XBZgJVF2YJDsjrCwMPpCztatW998802TngiYE3OURVYiJEJI\nzIBN4vP5raZswOBwcBwaLpfLtXcGtIOLUFhaCx2AQbI7Lly48OjRI+plaWnp1atXTXoiYGsQCMW1\n2KRW7Y0IIUXLsVSjTcLWRSgUardJ1HYlvEUJbJINY18GyeIpy7SQeFwhL6zgf5HFSfiN/0WWvLAi\n8bhC92kAE7B5YLAUosUmyTTYG+Jlm9TaGhA2NgKBQCgUyuVyjZcCm2Q32Nc+JHN4MwxCvPuG7Fwp\ncd5FWf6iBgEuEoEQkozVtEvehDx+/Pjo0aPUy9DQ0L59+5pfDbMRHx/P/kTIrINo2W8kQwhpSMOq\nQEhI25+kloII7z0iCEIsFotEIi1blDIyMsRisVwuxzYpNTVVIBAwcBcAm7Avg8RaJFF82blSyhpR\nB6MCu1hEH6VSSc88lpycbNsGCTAcalcs0mCTMmg2SYmQWlZVgiDi4uIQQtp3whIEkZqampaWhrfN\nisVilfx4gA0ABskkyM6VJp4w1uFGuLm0tda4aIhPW2dUz549U28cPHiwzv0irZ4IWBzT1VjRiP42\nSY4Qn+bKo7rQcjQgrTYJmy5skxITE2/fvg2pHPQE6iHZL7fLa6lZjsEYL6FVOnbsWFJSQr3MztZW\nZJaREwFzYhm/tIT2vzoEzSYpW7dJyKD0Qto7A3Ssoh4SGCSTEODm0tbq4Ormx0T1xQcOHJiWljZm\nzJgePXp8//33Fy5ccHNzw2+lp6cPHDjQw8OjrSdWV1dnZ2ePHj3aFAoD1oF2o0Co2aTW8uNJJJKA\ngACdjji66QKbZEuAQTIJohAfUYiP/v3lhRVUFAOd1Nh+gp485vRCCKG1a9e+9dZbw4cPb9eu3YQJ\nExITEzdseFE4dsqUKdu3b584cWJbT7x9+/aUKVMqKiqYVRWwKYiXbZKQ9pL4c86k57IQ2CSbBAwS\nKzhZUKneqMR+v54MX2vw4MG3b98uLi7m8XivvPIKQmjhwoUmPREAXkCo2SQjwNMpnFUIe/CobEOA\nlWJf+5BYi2QsXxrFz5jzGnbTEW4uimVhqbH92jTN0h8Oh+Pv74+NCoMnrlu3zsvLy93dff78+Ubr\nCFg5fA1l/QiEMhASIIRazJIRqKQX4vMtsEcCYBCYIbEFHB2nWBZGtYjcTGKNTERVVVVubm5ubm5B\nQYFAIHj77bdHjhyppf/Dhw8/++yz+/fvh4WFzZ8/n8vlIoS+++67xsZGhNDbb7+taSkLsA7wTKjV\ntSKitZxDlClRi3fg8/laiprj9EJ4t6xSqdTeGWA5MEOyZRYvXvyXv/xF/dgUkCT59ddfu7u7h4aG\nhoeHFxQUaNdh06ZNK1eu3Llz56VLl4RCYW1t7cKFC8PCwubMmTNnzpwff/zRdKraNmzJOkG0bDkS\n6jENUtL+qbyjVBIEAakcjMcqkqtCCXMrEG42unTpcvjwYQNOvHbtWufOnamX48aN++6777T0v3Ll\nyo0bN6iXERERvXr1ysrKolpu3LhB74CBJ6gT1t2FoqX8ueLldqLlH6L901AoHZc216cCOjUxwtMm\nxu7ChmDdCHkZmCEBzMDhcPTvXFJS0r17d+rlt99+e+vWrZycHKrFw8OjtLSUSf0Ai0BomCcpWv4R\nL/dvLSgB74cViUQymUxLsT4qMx5qmSdpmVQB7AQMEmABxowZc+TIEerlV1999fPPPy9evPjkyZO4\n5eDBg9qXoACrgWhZRtLpu1NqTB+O98OKRCLtBWRxeiGqArpYLIZqs9aFfQU1WCCrCtAaDg4Onp6e\naWlpHTp0+PXXXz/66KMePXr88ssv77333uDBg7lc7ltvveXgYL7ByZZ1F1uFQCgVoUSEhK3naEAE\nQiKEpLQ0rK3tKTIgvZD2/HgA67C0z9B8wAoE22hqaqqpqVFpfPbsWVNTU6v94QnqhNV3odDVQUpb\nT9K8WoQ3G4lEIh3CpFLqW0774pNdweoRQpL2NUMCWAWXy3VxUU2P1KFDB4soA5gcQlcHepJWKa3l\nZUQikUAg0BnYDakcrBFYQwIAgDVI9Cp/ruc2I4lEQuVu0L74BLAEMEgAALAJkV42SV9hIlFGxosS\nTFKpFOcZAlgLGCQAsCmsKUCDo8HeiHSXP1dBy05YgUBAbVGy5/RCVrExFgwSANgU1hRHKtU8ByJo\nNkmm2ya1KZUDn8+3w1QO8fHxeXl5ltZCB2CQAACwEHjFSKrVJhEIIYRkGlK1IoQQUiqVIpFI+64j\nSC9kFYBBAhigpqbm2rVrlZWtFNEAAG2IWmxSq3MggpabVYkQv/WttQancgCbxDbAIAHGsmnTJl9f\n37i4OIIgPvnkE0urA1gbIoQUmv1yxMs2SUO6hzalcsA1ACG9EBux9EYo8wHbKk1BTk7OK6+8kp+f\nT5KkUqns3LlzZmamia4FT1AnVnwXipb8qpreJWg5WBUaxVAbj7RdSqGgts3qzNlqY7B8hMAMCTCK\nq1evjhkzplevXgihgICAwMBAqvAEALQBoiWKQZ+yfprT4uG9R9ojvLGLj0p5p93RB5gVS1tE8wG/\nr01NXl5e+/bt1ctGMAU8QZ1Y/V0odL0r0muehMvICgQC7Vezw/RCLB8hMEOyFxQKxaVLl0wXd5CZ\nmRkREbFs2bK+ffua6BKA7UPoelfSklVIiZCwtcqzuCNBKBQKakusJiQSCWWTIJUDGwCDZOPU1dXN\nmzePx+P16NEjODjYzc0tOjoa/37UH2dn523btml6t76+ftGiRVOnTk1KSlq2bJnRKgOAZgiE4mg2\nSUO5CgTphawTMEi2TE1NTXh4+I4dO1avXl1YWFhYWLh+/frs7OzIyMhHjx4xdZXJkycrlcrr169H\nR0czJRMAXqBUayFenifJGEgvRP1Eg/RClgUMki2zcePGy5cvy+Xyf/zjHz169OjRo8f8+fOTkpIK\nCwu3bNnCyCUOHjyoVCr/+9//dunShRGBAPASmvxybbdJ2lM5QHohNgAGyWYhSXLVqlWTJ09+7bXX\n6O2TJ09es2aNr69vm6Q9e/bsgw8+cHNz8/T0FIlET58+xe2//PJLbm5uhw4dnFvYv38/Y/cAtB1r\nymWnEyVCIoTEetgkqQ6blJiY2KZUDraXXsgqctnZV5RdUlKS6YSbSLLB3Lt3DyEkk8mMF+Xk5OTj\n4zN+/PgdO3YkJCQ4OTktWbLEeLFtxXQfclJSEgufoAHYxl28hIIkpSRJaC7Zp19ZP7z3SOeuI2qe\nhFqmTUaozkZYPkLsyyBZqXDDOHnyJELot99+M16Uk5PT8OHDqZeTJk0aMmSI8WLbir09QQOwjbtQ\nRaHLJqXqZZNIvbfN4vRCNmmTWD5CoGKsSWgou6vlXUdPfxP1V+9ZX1+vRbL+TJo0iToODg6+cuUK\nI2IBQDdES+lYGUKotTKyIoRQS+YhqYY+uJlWRlZTAVmcXigtLU0qleL0QqmpqZSJAkwKGCSTUCXf\n+3jvWk3v9t5XotKimBOqRZr+/d1jEtxjEvAxXpi9c+eOerddu3aVlJQkJCRouagKXbt2pY45HA5J\nkvqfCwAMQC9w3qpNErRkeZAipKRV+VMRI5EEBATgUDotNikuLg4hhG2SWCwWiURQAd0MgEEyCa6C\nGFdBjP79+Zuy2yRfU3/6DMnPz4/H4x06dOi9995T6bZixQorWN4EABW02yQCIUVLViEZQkqENOyL\nFYlEBEHgbN/UJiRVYQRBTadweiGk2YABTAEGySSou87M35/L5c6fP//TTz89ffr08OHDqfb09PSc\nnJwFCxa06YoAwAoktP/VIRDKaLFJcoT4tCp/L4PLyAqFQh1Xo9kk7Y4+gBEg7NuWWbBgQc+ePSMj\nI7/99tuCgoKHDx/+8MMPMTExw4YNU9n9V1VVVVRUZCk9AaANaLcIhF4llFBLwILuq72cXkgsFsvl\ncj6fz+Fw+Hy+XC6H5A4MAjMkW4bH450/f3727NkJCQnPnj1DCHG5XLFYvHLlSi73pd8iiYmJjx8/\nxn4JALBuCNo8Sfn/7d17VBTX/QDw7woComLAA4KozPoADQQfFFBEXVBiW1+J+ApVWVPT2qpJGvUk\njTG7tGmbqlHDI54mKoueqD9rPFGCbXwBxohifKGSguIOGkEpKEURkJX5/THZyQg7sw92mdf3c/hj\nd/Yyc3e58OXeufd7ARJYIcoh7NtOBoOhoKCAWaLE9LGw5+QU2EOSuT59+uzevbuhoaG0tPTKlSuN\njY3btm1jz1B4//334+PjN23axHOSlpaWV199lXn63nvv2ZsND6EuRdi0rZ/t2OmFmGjEPJg0aVKn\nzo7MMCApQrdu3UaMGBEREeHl5dXupSlTpqxbt47eQxMh6VF1dgslNv5UDlzHMf2ds2BAUrqJEydO\nnTqV3mEPIenh39Yv26btKmhpaWkObNZHkqTMkgwJCO8hIYSkjDDfMVJbuldEAKQCgHlx0hKAbHO3\nqQOry2YJgugYe2zc5wLZAntICCGJI8xLjiyOyxG2bqEE5jl1XBsjcS1a4jqO7IUBCSEkfYS1mGTz\ndhU8MYnOD9kOncqBZ28LZDsMSAghWSDMQ3Zc8xfsiUn5+fkdN+ujYxWzSwWYx/fomIQLkjoPAxJC\nsiKr/ZDsRQBkm2OSRTZvoUSncqDXwD5zAp2OfonOTs0sm6XTC4k5JuF+SOKCmxdIHf4ErZLHu+gs\no7UCtm2hRJm3R7J6QSaVA1jb20JwIm8h2ENCCMkLYa2AjpULXM/XT3IsvZCY+0kihwEJIaQ8WlYu\ncL15L6VO0Ol0zFw7jEkOw4CEEFIkDSsXuMEJMYmdXqjjhAhkCwxICCG5U3GMyxEARvMQn4Ej3cOz\n1Go1f3oh+rYTABgMhnYTIpBVGJAQQnKn575XRHTYroKXVqvln01HEAQzL5wkSbVajYmFbIcBSc5a\nWlqePn3a8bFcr4uQZTo7YxLJfSadTqvV8t8laheT6K1pHay5wmBAkrPJkycfOnSo42O5XhchTjpz\nolVbYhJvanD+9EI/ng9jkkMwICGElEELkM89p46wY7sKek4d/8wFOiZpNBowxyRML2SVsgKSohex\nI27YMJRCA2AEMHCkciBYucBJKzGJnlPHP3OBIAg6boE5vRBuysxPWQFp5cqVQlcBiRE2DAUhAIzc\n8xcIO7ZQYpbN8sek1NRUJialpaXhEiUeygpICADi4uLYN3W2b98+a9YspxRGSBoIgHzWIqSOr7bb\nrsLAfSaCyM/P58/mQBCEhFLeCQsDkrio1WqVSuXS5Qvnz5+vra1lnlZXV5eUlDilMEKSQVh7lR2T\n0qykF7LlguyYhKkcuGBAQgihDgg7tquwEaa8swq3MEc/qqur++qrr5insbGxw4cPF7A+CHUp0lK3\nid7HXG/eroI54iidThcSEkLPzePZK12xMCCJAjNGxyxWYI7YkmzYKUiS1Gq1zNOMjAwMSEgp6Al1\n+bwxCWyNSWq1WqvVckUarVar0WjoX3C9Xk+SJO6AzsCA5BL23rdst2iO/dSu+0k8vwZcGhsb6QdR\nUVEURdlYGCFZyQZIA0hgTftm0wGEmFcv6QEAwGDuUVn6d5FO5QDcvR96eh69WtZgMBQUFHTZ/50i\nhwHJJSorK521MNvpC7x79uxZVVXFPD179qyzCiMkVQSADoAAWAKgA9B2KEAfYcckbnQcshqT8vPz\n6ZhEp7xj74yuWBiQXCIkJMSxtsWEH9c1zcjIyJycnClTpgwePPizzz47f/68n5+fA4UfPXp09uzZ\nyZMnu6ieCHUpAiAVAADSACotjctpATQ2ZQQH1r0inhG5djEpISEBYxJuYS6uk9PN0ZZdk20xfvz4\nAwcOtHv83XffDRw4EADc3NxmzZq1efNmnsvxFL569epzzz1n+3U7TxI/QWHJ410ITE9RBMfW5gRr\n73OgKIL1ZQk9EMf/62w0Gun0QmAeyuv8O+Ah8haC074VJyoqqrKy8tatW/X19V9++eWbb77JM35t\nV2GE5IAestNbmudNdnjKfFnCTuXANfZOpxei5xNhyjsMSOJC/3/k6j/6KpVq4MCBvXr16nzhTZs2\n9evXr2/fvq+//rpT64gs2LFjx6xZs6ZPn75t2zah6yJrzHYV7RDmr47HOdDjcgCQkGAxfd6PZdjL\nZpcsWaLYJUp4Dwk5rqGhobS0tLS09MaNGxqNZu7cuRMmTBC6UrJ1+vTpf/3rX3v37n369GlKSkpk\nZGRMTIzQlZIvi3MRmH8UO+6ZRHKGJfZWFFzolHdgnghO52BV4BIl7CHJ2erVq0eNGtXxsbNQFLV5\n8+a+ffvGxsaOHz/+xo0brr4ueb/ZWaeSnOrq6pSUlB49evTq1euFF164ffu20DWSO1vCgQYArKcG\nt2WqQrt+kjJTOWAPSc5eeukli4+dxcfHp3fv3vRjT09Pk8nk6usmbL1gXBvnxBNKSHJyMv2gqqrq\nm2+++d3vfidsfdCPqcGXABSYY5LFpbX2YE8ZV2AqB+whIcepVKouviJ5vznta5nMqnj06FG7Xk5z\nc/P169cbGhqYI6dPn9bpdDqdbufOnfSREydO0OsuBwwY0KXVRWxGAArAaN92FWw8vR8lp7zDgIQk\nxvBddUHFA6Fr4QSZmZlZWVnM09zc3AkTJqxevTohIWHDhg30weDg4Pj4+Pj4+IiICAD48MMPd+/e\nnZOTk5iYKEyllUzFvYVSu+0qbIgg/JGG3pGWKcmzL63MYEBCEkPeb16y93uha9EpH3/88SuvvMJe\nL1lfX//ee+9lZmYePHjw3//+9/79+0+fPg0AISEhSUlJSUlJY8aMOXbsGEmSn332WVBQEM/Jw8LC\nwsLCcA9c56N75lwxyc7U4Hq9nj8m0TvS0o8NBgPPJD2rMjIywswcPknXwHtIyEHh4eEPHvzUU8nL\ny+uCi2qjgwznqumYlL1gRBdc0RXi4uKioqLy8vIoc/LA4uLiwMDA2NhYAPD3909MTDx58mRc3DN3\ny44ePVpaWjpjxgz66erVq5kFlWxlZWWurb1iEQD5AAkAamtpWBN8xi0AABhzSURBVEnraVhtTOXA\npLwrKChQq9WOLQhZuXIlsyeyyGMSBiQkJboX1QUVD8j7zYZz1anRgZohvkLXyBHR0dEAcPXqVWax\n5L1799j9nsDAwMrKynbf9fe//72rKog4EOaYxDV/wZ7U4Ezab57kqkpLeYdDdkhKCD8vpmO0ZO/3\nspkFbjKZ3NzcmKfu7u6tra0C1gdxIgDyAYB7nrcOgOnw6K2M3dmYyoEJQnQqB6cnXBYPDEhIYjRD\nfPUvquHHm0mlQlfHOTw9PZubfwquTU1Nnp6eAtYH8SHM3SOumKR9Nibxzkhgp3Lgj0n0CK28YxIG\nJCQ9qdFBmiHPAUBBRb08ZoEHBwez/8QYjUaHZ3XjdIauQABkm2OSRVpWWgeDHTGJp0x2djazbNaB\nlHf01Aa7vqXrYUBC0kP4eWUveJ5+bPiuWgYDd9HR0S0tLXv37gWAa9euFRYWOjyrirl9jVyLAMi2\nvEHfTwWM5vtMBiv7VtAxiX/OAp1eyOGUdytXrhT/hBcMSMg5Ghoabt682WWXY24mkfebE7Ze6LLr\nuoi3t/f69eu3bNkSFxe3YMGCFStWjBw5UuhKIWsIGwowcx9ISxnw2GXtTy9k787U4oez7JBzpKWl\n1dXV0Ukhu4Y2OijnXHVBRT2dvkE31Y693sVg2bJl7KeJiYlFRUW1tbW+vr7u7viLKReEeWIe6fz0\nQnTKO5BReiHsIaHOev/99+Pj4zdt2tT1l2YP3MkgfYNKpfL398doJDfEs/0k3jSsbApML4QBCXXW\nlClT1q1bR+8w1sXYA3dST9/gLDipQUgqjnneBEC+ranBaWlpaXalF7Iak3BSA1KEiRMnTp06ddiw\nYYJcXRsdpI0OAoxJZjipQUh67rVHhH1pWOl4w5/ITqvV0tPzwIaUdzipAYmI0Wi8ePFifX290BVx\nPt2LasLPCwAM56oN56qFrg5SMJ21mGRPGlY6nZ3BYFCrOe+PajQadso7npKSgAFJ5lpaWlasWOHr\n6zt48OAxY8b4+fnNnj3b3oxYnp6eO3bscFENO4+dviHtiFEGs8CRhOn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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Pure Dirichlet boundary condition.\n",
    "mesh.bdFlag = setboundary(node,elem,'Dirichlet');\n",
    "mfemPoisson(mesh,pde,option);"
   ]
  },
  {
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   "source": [
    "## Conclusion\n",
    "\n",
    "The optimal rates of convergence for $u$ and $\\sigma$ are observed, namely, 1st order for L2 norm of u and H(div) norm of $\\sigma$. The 2nd order convergent rates between two discrete functions $\\|u_I - u_h\\|$ is known as superconvergence. Compare with RT0, the L2 norm of $\\sigma$ is 2nd order.\n",
    "\n",
    "Triangular preconditioned GMRES (the default solver) and Uzawa preconditioned CG converges uniformly in all cases. Traingular preconditioner is two times faster than PCG although GMRES is used and iteration steps are doubled."
   ]
  }
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     "text": "MetaKernel Magics",
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